This approach involves creating a basic Trie data structure using a tree of nodes. Each node represents a character in a word. Starting from a root node, each character of the word is inserted sequentially, with branches representing the progression to subsequent characters. This forms a chain of nodes (linked in a tree-like manner) from the root to the nodes representing complete words. For searching, we traverse these nodes based on the characters of the input word or prefix to check for existence.
Time Complexity: Insert, search, and startsWith operations are O(m), where m is the length of the word/prefix.
Space Complexity: O(26 * n * m) in the worst case, where n is the number of inserted words and m is the average length of the words. Each insertion can potentially add m nodes with 26 possible children each.
1class TrieNode:
2 def __init__(self):
3 self.children = {}
4 self.is_end_of_word = False
5
6class Trie:
7 def __init__(self):
8 self.root = TrieNode()
9
10 def insert(self, word: str) -> None:
11 node = self.root
12 for char in word:
13 if char not in node.children:
14 node.children[char] = TrieNode()
15 node = node.children[char]
16 node.is_end_of_word = True
17
18 def search(self, word: str) -> bool:
19 node = self.root
20 for char in word:
21 if char not in node.children:
22 return False
23 node = node.children[char]
24 return node.is_end_of_word
25
26 def startsWith(self, prefix: str) -> bool:
27 node = self.root
28 for char in prefix:
29 if char not in node.children:
30 return False
31 node = node.children[char]
32 return TrueIn the Python implementation, we make use of a TrieNode class with a dictionary to store pointers to child nodes and a boolean attribute to denote if the node is the end of a word. The Trie class creates the root node as part of the constructor. The insert method processes the word character by character, adding nodes for characters that are missing in the current sequence. The search and startsWith methods traverse down the trie nodes based on the characters of word or prefix, verifying each node's presence accordingly and checking the is_end_of_word flag when necessary for search.
This approach relies on maps (or hashmaps) for storing children nodes dynamically. The advantage of using maps over arrays in this context arises from reduced space consumption when handling sparse trees since only existing characters are stored. Nodes manage their children using hash references, leading to more flexible branching.
Time Complexity: O(m) per operation where m is the word/prefix length.
Space Complexity: O(n * m), where n estimates the word count and m accounts for varying lengths since nodes only maintain necessary mappings.
1class TrieNode {
2 constructor() {
3 this.children = new Map();
4 this.isEndOfWord = false;
5 }
6}
7
8class Trie {
9 constructor() {
10 this.root = new TrieNode();
11 }
12
13 insert(word) {
14 let node = this.root;
15 for (let char of word) {
16 if (!node.children.has(char)) {
17 node.children.set(char, new TrieNode());
18 }
19 node = node.children.get(char);
20 }
21 node.isEndOfWord = true;
22 }
23
24 search(word) {
25 let node = this.root;
26 for (let char of word) {
27 if (!node.children.has(char)) {
28 return false;
29 }
30 node = node.children.get(char);
31 }
32 return node.isEndOfWord;
33 }
34
35 startsWith(prefix) {
36 let node = this.root;
37 for (let char of prefix) {
38 if (!node.children.has(char)) {
39 return false;
40 }
41 node = node.children.get(char);
42 }
43 return true;
44 }
45}The JavaScript version utilizes Map for storing node child references. Map is advantageous with its guaranteed key storability and inherent ordering. The insert method tracks through characters, setting or accessing nodes on the fly with hashmap properties. Searching evaluates characters' existence in path while confirming final node's end-markers during search. Prefix check seeks each character similarly ensuring entire path viability.